quadric
/'kwɔdrik/
Definition
- Noun:
- A curve or surface whose equation (in Cartesian coordinates) is of the second degree: In mathematics, a "quadric" is a geometric shape, such as a curve in two dimensions or a surface in three dimensions, defined by a polynomial equation where the highest sum of exponents in any term is two.
Examples of Usage
- Noun:
- The sphere and the ellipsoid are common examples of a quadric surface.
- In algebra, we learned to classify conic sections, which are types of quadric curves.
Advanced Usage
"Quadric surface": A specific term for a three-dimensional quadric.
- The paraboloid is a quadric surface used in the design of satellite dishes.
"Degenerate quadric": A quadric that simplifies into a lower-dimensional shape, like a pair of lines or a single point.
- When the discriminant is zero, the equation may represent a degenerate quadric.
Variants and Related Words
Quadratic (adj): Pertaining to the second degree or involving terms up to the square of a variable.
- A quadratic equation is related to the concept of a quadric curve.
Quadric cone (n): A specific quadric surface shaped like a double cone.
- The equation x² + y² - z² = 0 defines a quadric cone.
Quadric cylinder (n): A quadric surface that extends a two-dimensional conic section along an axis.
- A parabolic cylinder is a type of quadric cylinder.
Synonyms
- Second-degree surface/curve: A descriptive synonym emphasizing the defining polynomial degree.
- Conicoid: A less common term, especially for quadric surfaces.
Related Idioms or Phrases
(This term is highly technical and specific to mathematics; it is not commonly used in idiomatic expressions or phrasal verbs.)
Noun
-
a curve or surface whose equation (in Cartesian coordinates) is of the second degree
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